The static approximation of heavy-light quark systems. A detailed lattice study

Abstract We present a study of finite a and volume effects of the leptonic decay constant ƒ of heavy pseudoscalar mesons in the static approximation. This study is performed on a number of lattices at β = 5.74, 6.0 and 6.26 covering sizes from about 0.7 fm to 2 fm, and the issue of the wave function dependence of ƒ is addressed. We confirm that beyond 1.5 fm the volume dependence is negligible. We also give results for the mass difference of the scalar-pseudoscalar and the Λb-pseudoscalar. Using the mass of the pseudoscalar meson we estimate the distance of string breaking in the static quark potential.